Remarks on symmetry analysis of Lane-Emden systems of dimensions one and two

Some recent results on Lie group analysis of the one and bi-dimensional Lane-Emden systems are revisited.Alguns resultados recentes sobre simetrias de Lie de sistemas de Lane-Emden uni e bidimensionais são revisitados.245254Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Lie Symmetries and Criticality of Semilinear Differential Systems

We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers

Group Analysis of the Novikov Equation

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilations symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigat the invariant solutions

Conservation laws for self-adjoint first order evolution equations

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

Numerical Ricci-flat metrics on K3

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.Comment: 38 pages, 10 figures; program code and animations of figures downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor corrections, references adde

Lack of Trehalose Accelerates H2O2-Induced Candida albicans Apoptosis through Regulating Ca2+ Signaling Pathway and Caspase Activity

Trehalose is a non-reducing disaccharide and can be accumulated in response to heat or oxidative stresses in Candida albicans. Here we showed that a C. albicans tps1Δ mutant, which is deficient in trehalose synthesis, exhibited increased apoptosis rate upon H2O2 treatment together with an increase of intracellular Ca2+ level and caspase activity. When the intracellular Ca2+ level was stimulated by adding CaCl2 or A23187, both the apoptosis rate and caspase activity were increased. In contrast, the presence of two calcium chelators, EGTA and BAPTA, could attenuate these effects. Moreover, we investigated the role of Ca2+ pathway in C. albicans apoptosis and found that both calcineurin and the calcineurin-dependent transcription factor, Crz1p, mutants showed decreased apoptosis and caspase activity upon H2O2 treatment compared to the wild-type cells. Expression of CaMCA1, the only gene found encoding a C. albicans metacaspase, in calcineurin-deleted or Crz1p-deleted cells restored the cell sensitivity to H2O2. Our results suggest that Ca2+ and its downstream calcineurin/Crz1p/CaMCA1 pathway are involved in H2O2 -induced C. albicans apoptosis. Inhibition of this pathway might be the mechanism for the protective role of trehalose in C. albicans